Spherical functions on symmetric spaces of Friedberg-Jacquet type

2023/10/31 by Corato-Zanarella, Murilo
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2311.00148

Abstract

We give explicit models for spherical functions on p-adic symmetric spaces X=H\backslash G for pairs of p-adic groups (G,H) of the form (U(2r),U(r)× U(r)), (O(2r),O(r)× O(r)), (Sp(4r),Sp(2r)\timesSp(2r))), (U(2r+1),U(r+1)× U(r)), and (O(2r+1),O(r+1)× O(r)). As an application, we completely describe their Hecke module structure.

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